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A179692
Numbers of the form p^9*q where p and q are distinct primes.
11
1536, 2560, 3584, 5632, 6656, 8704, 9728, 11776, 14848, 15872, 18944, 20992, 22016, 24064, 27136, 30208, 31232, 34304, 36352, 37376, 39366, 40448, 42496, 45568, 49664, 51712, 52736, 54784, 55808, 57856, 65024, 67072, 70144, 71168, 76288, 77312, 80384, 83456
OFFSET
1,1
LINKS
MATHEMATICA
f[n_]:=Sort[Last/@FactorInteger[n]]=={1, 9}; Select[Range[90000], f]
PROG
(PARI) list(lim)=my(v=List(), t); forprime(p=2, (lim\2)^(1/9), t=p^9; forprime(q=2, lim\t, if(p==q, next); listput(v, t*q))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 24 2011
(Python)
from sympy import primepi, integer_nthroot, primerange
def A179692(n):
def bisection(f, kmin=0, kmax=1):
while f(kmax) > kmax: kmax <<= 1
kmin = kmax >> 1
while kmax-kmin > 1:
kmid = kmax+kmin>>1
if f(kmid) <= kmid:
kmax = kmid
else:
kmin = kmid
return kmax
def f(x): return n+x-sum(primepi(x//p**9) for p in primerange(integer_nthroot(x, 9)[0]+1))+primepi(integer_nthroot(x, 10)[0])
return bisection(f, n, n) # Chai Wah Wu, Feb 21 2025
KEYWORD
nonn,changed
AUTHOR
STATUS
approved